What is a heavy node in neural networks?
Yes, firstly you are correct to acknowledge the term node with reference to the neural network.

A neural network is made to mimic the working of a human brain hence the term neural. It comprises of several layers and each layer comprises of several nodes. A network can be a deep neural network, signifying the presence of numerous layers, in which the output of the one, serves as an input for the other.
Further a node in a particular layer has some weights and biases attached with it that are responsible for the computation and producing output.

To your context, a heavy node may refer to a node that holds importance for the network and has got significant weight and bias attached. Henceforth as per the statement if the network does make any significant change to the node with importance in terms of weights and biases, it is noticed else not.